A store’s cash drawer has five slots for currency: $1 bills $5 bills $10 bills $20 bills $50 bills & $100 bills together A customer buys an item that costs $114, and she pays $120 (with a $100 bill and a $20 bill). She gets $6 in change (a $5 bill and a $1 bill). This transaction used four of… Read more →

A local nursery is discounting shrubs and bushes. A 1-foot diameter shrub is only $1. A ½-foot diameter shrub is $2. The ¼-foot diameter shrub is $4. (And so on… one-third foot diameter = $3, one-tenth foot diameter = $10.) What is the cheapest way to fill the greatest area of a flowerbed that is a 4-foot square? How much… Read more →

If my purchase at the store totals $4.97 and I pay with a $5 bill, I get 3 coins back. If I give the cashier a $5 bill plus two pennies, I get 1 coin back. How can I use this transaction to consolidate my change into the fewest coins possible? When should I give the cashier a few extra… Read more →

I love those rich conversations with colleagues when they express a thought and you feel like you agree completely, but you’ve never been able to express it that clearly. That’s how Routines for Reasoning makes me feel – the book explores strategies teachers can employ to help develop students’ reasoning and problem-solving abilities. Each of the strategies does such a… Read more →

A new Mondo-Lotto Lottery Game is a scratch-off ticket with a three-by-three grid. Each section has an X or an O – just like Tic-Tac-Toe. If you scratch off the same three symbols in any row, column, or diagonal, you win a prize. What is the fewest number of sections you might have to scratch off to know your ticket… Read more →

Twelve is the largest number that is only one syllable long. “Twenty-four” is three syllables, but so is “eight times three,” which is also equal to twenty-four. What is the greatest value expression or number you can write with five syllables? What is the smallest value you can create with five syllables? Can you create an expression whose value is… Read more →

Twitter-Length Tasks can be quickly and simply explained, yet allow for extensive exploration. Both hands of a clock are constantly moving. The small hour hand only points directly at a number when it is the top of the hour. Otherwise, that hour hand keeps moving around. So at 7:30, the hour hand is halfway between 7 and 8. So at 3:00,… Read more →

Twitter-Length Tasks can be quickly and simply explained, yet allow for extensive exploration. In the equation 4 + 6 = 10, each number is written in alphabetical order: four + six = ten In the equation 3 – 1 = 2, the numbers are not in alphabetical order: three – one = two Can you come up with one example of… Read more →